Question

for a segment of a radio show, a disc jockey can play 5 records. if there are 8 records to select from, in how many ways can the program for this segment be arranged?
□ ways

Explanation:

Step1: Identify permutation scenario

We need to arrange 5 records out of 8, where order matters. The permutation formula is $P(n,r)=\frac{n!}{(n-r)!}$, where $n=8$, $r=5$.

Step2: Substitute values into formula

$$P(8,5)=\frac{8!}{(8-5)!}=\frac{8!}{3!}$$

Step3: Expand factorials and simplify

$$\frac{8\times7\times6\times5\times4\times3!}{3!}=8\times7\times6\times5\times4$$

Step4: Calculate the product

$8\times7=56$; $56\times6=336$; $336\times5=1680$; $1680\times4=6720$

Answer:

6720